不完全市场下考虑损失厌恶的连续时间投资组合选择

摘要

In this study we investigate a general continuous-time portfolio selection model with loss aversion in an incomplete market where the number of stocks is strictly less than the dimension of the underlying Brownian motion. The investor's preference facing market risks is defined by a S-shaped value function.By transforming the market into a complete one,we solve the optimal terminal wealth and the optimal wealth-portfolio pair of agents using martingale method and replicating technique.A special example with a two-piece power function and deterministic coefficients is presented to illustrate the general results.Last,the explicit expressions of the optimal solutions are given.%在不完全市场条件下研究了一般情形下的损失厌恶投资者的连续时间投资组合选择模型.面对市场风险,投资者的偏好由一个S-型的价值函数定义.通过把不完全市场转换为完全市场,利用鞅方法和复制技术,分别获得了投资者的最优期末财富以及最优投资策略.最后讨论了一个分段幂函数的例子,在模型系数为确定的常数情形下,得到了最优解的显示表达式.